BOSTON, Dec 3 (Reuters) - A group of U.S. fraternities and sororities on Monday sued Harvard University, saying its crackdown on single-sex clubs amounted to sexual discrimination.

In lawsuits filed in federal and state courts in Boston, the group challenged a policy that the Ivy League university adopted in 2016 and began enforcing this academic year that Harvard said was intended to end longstanding practices of exclusion at the elite school.

Harvard has long sought to stamp out single-sex clubs, which it stopped formally recognizing in 1984. But groups known as "final clubs," informal social clubs a student joins before graduating, as well as some fraternities and sororities have continued to operate off campus.

Under the policy, students who join single-sex clubs may not serve as captains of sports teams or leaders of officially recognized student clubs and cannot receive endorsement letters from college deans for postgraduate fellowships.

The Cambridge, Massachusetts, university was discriminating against students on the basis of their sex by punishing men and women who join all-male or all female-organizations, the lawsuits alleged.

The policy was motivated by sexism, with Harvard incorrectly seeking to link all-male organizations and fraternities to sexual assaults and contending that single-sex organizations subordinate women, according to the lawsuits.

"Harvard's sanctions policy seeks to dictate the sex of people with whom men and women may associate and the gender norms to which men and women must conform," the federal complaint said.

The policy has resulted in the elimination of nearly every women's social organization, with Harvard administrators privately calling them "collateral damage" in their effort to punish men who join all-male groups, according to the complaint.

"Harvard should get out of the business of trying to dictate who students spend their time with off campus," Stanton Jones, a lawyer for the sororities and fraternities, said in a statement.

Harvard had no immediate comment.

The federal lawsuit was brought by the fraternities Sigma Chi and Sigma Alpha Epsilon and the sororities Kappa Alpha Theta and Kappa Kappa Gamma, as well as three students.

The state court case was filed by the international sorority Alpha Phi and a local chapter, as well Delta Gamma Fraternity Management Corp, which supports chapters of the Delta Gamma sorority.

Harvard's policy violates Title IX, the federal civil rights law that bans discrimination on the basis of sex, the U.S. Constitution, the Massachusetts constitution and the state's Civil Rights Act, the lawsuits claim. (Reporting by Nate Raymond; Editing by Scott Malone and Jeffrey Benkoe)

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